This study will examine the effect of exenatide on body weight, energy expenditure, satiety, sleep, and metabolic parameters in healthy, moderately obese women (BMI 28-35 kg/m2). We will look at 2 populations of women, one with normal glucose metabolism and one with impaired glucose homeostasis (IGH)--either impaired fasting glucose (IFG, fasting glucose 101-125 mg/dL) or impaired glucose tolerance (IGT, glucose 140-199 mg/dL 2h after a 75g oral glucose load). This is a randomized, double blind, crossover study with two 16-week treatment periods separated by a 3-week washout period. There are 19 study visits over 35 weeks.